On the existence of initial data containing isolated black holes

Details On the existence of initial data containing isolated black holes On the existence of initial data containing isolated black holes

2004-12-13

arxiv.org/abs/gr-qc/0412061v1

Phys.Rev. D71 (2005) 064003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 2 figures, RevTeX4

Scientific paper

10.1103/PhysRevD.71.064003

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.

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